{"product_id":"the-finite-element-method-isbn-9781119107316","title":"The Finite Element Method","description":"\u003cp\u003eA comprehensive review of the Finite Element Method (FEM), this book provides the fundamentals together with a wide range of applications in civil, mechanical and aeronautical engineering. It addresses both the theoretical and numerical implementation aspects of the FEM, providing examples in several important topics such as solid mechanics, fluid mechanics and heat transfer, appealing to a wide range of engineering disciplines.  Written by a renowned author and academician with the Chinese Academy of Engineering, The Finite Element Method would appeal to researchers looking to understand how the fundamentals of the FEM can be applied in other disciplines. Researchers and graduate students studying hydraulic, mechanical and civil engineering will find it a practical reference text.\u003c\/p\u003e \u003cp\u003ePreface xxiii\u003c\/p\u003e \u003cp\u003eAbout the Author xxv\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction to Finite ElementMethod andMatrix Analysis of Truss 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Introduction to Finite Element Method 1\u003c\/p\u003e \u003cp\u003e1.2 Truss Analysis Overview 5\u003c\/p\u003e \u003cp\u003e1.3 Stiffness Matrix of Horizontal Bar Element 8\u003c\/p\u003e \u003cp\u003e1.4 Stiffness Matrix of Inclined Bar Element 10\u003c\/p\u003e \u003cp\u003e1.5 Coordinate Transformation 11\u003c\/p\u003e \u003cp\u003e1.6 Nodal Equilibrium Equation and Global Stiffness Matrix 14\u003c\/p\u003e \u003cp\u003e1.7 Treatment of Boundary Conditions 15\u003c\/p\u003e \u003cp\u003eBibliography 23\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Plane Problems in Theory of Elasticity 25\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Discretization of Continuous Medium 25\u003c\/p\u003e \u003cp\u003e2.2 Displacement Function 28\u003c\/p\u003e \u003cp\u003e2.3 Element Strain 30\u003c\/p\u003e \u003cp\u003e2.4 Initial Strain 31\u003c\/p\u003e \u003cp\u003e2.5 Element Stress 32\u003c\/p\u003e \u003cp\u003e2.6 Equivalent Nodal Force and Element Stiffness Matrix 35\u003c\/p\u003e \u003cp\u003e2.7 Nodal Loads 40\u003c\/p\u003e \u003cp\u003e2.8 Nodal Equilibrium Equation and Global Stiffness Matrix 43\u003c\/p\u003e \u003cp\u003e2.9 Establish the Global Stiffness Matrix by the Coding Method 48\u003c\/p\u003e \u003cp\u003e2.10 Calculation Example 51\u003c\/p\u003e \u003cp\u003eBibliography 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Element Analysis 53\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Principle of Virtual Displacement 53\u003c\/p\u003e \u003cp\u003e3.2 Element Displacement 56\u003c\/p\u003e \u003cp\u003e3.3 Element Strain and Stress 57\u003c\/p\u003e \u003cp\u003e3.4 Nodal Force and Element Stiffness Matrix 57\u003c\/p\u003e \u003cp\u003e3.5 Nodal Load 59\u003c\/p\u003e \u003cp\u003e3.6 Application Examples of the Principle of Virtual Displacements: Beam Element 61\u003c\/p\u003e \u003cp\u003e3.7 Strain Energy and Complementary Strain Energy 64\u003c\/p\u003e \u003cp\u003e3.8 Principle of Minimum Potential Energy 65\u003c\/p\u003e \u003cp\u003e3.9 Minimum Complementary Energy Principle 69\u003c\/p\u003e \u003cp\u003e3.10 Hybrid Element 70\u003c\/p\u003e \u003cp\u003e3.11 Hybrid Element Example: Plane Rectangular Element 73\u003c\/p\u003e \u003cp\u003e3.12 Mixed Energy Principle 75\u003c\/p\u003e \u003cp\u003e3.13 Composite Element 77\u003c\/p\u003e \u003cp\u003eBibliography 79\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Global Analysis 81\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Nodal Equilibrium Equation 81\u003c\/p\u003e \u003cp\u003e4.2 Application of the Principle of Minimum Potential Energy 82\u003c\/p\u003e \u003cp\u003e4.3 The Low Limit Property of the Solution of Minimum Potential Energy 84\u003c\/p\u003e \u003cp\u003e4.4 The Convergence of Solutions 85\u003c\/p\u003e \u003cp\u003e4.5 Analysis of the Substructure 88\u003c\/p\u003e \u003cp\u003eBibliography 91\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 High-Order Element of Plane Problem 93\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Rectangular Elements 93\u003c\/p\u003e \u003cp\u003e5.2 Area Coordinates 97\u003c\/p\u003e \u003cp\u003e5.3 High-Order Triangular Element 100\u003c\/p\u003e \u003cp\u003eBibliography 104\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Axisymmetrical Problems in Theory of Elasticity 105\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Stresses Due to Axisymmetrical Loads 105\u003c\/p\u003e \u003cp\u003e6.2 Antisymmetrical Load 110\u003c\/p\u003e \u003cp\u003eBibliography 114\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Spatial Problems in Theory of Elasticity 115\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Constant Strain Tetrahedral Elements 115\u003c\/p\u003e \u003cp\u003e7.2 Volume Coordinates 121\u003c\/p\u003e \u003cp\u003e7.3 High-Order Tetrahedral Elements 122\u003c\/p\u003e \u003cp\u003eBibliography 124\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Shape Function, Coordinate Transformation, Isoparametric Element, and Infinite Element 125\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Definition of Shape Functions 125\u003c\/p\u003e \u003cp\u003e8.2 One-Dimensional Shape Functions 126\u003c\/p\u003e \u003cp\u003e8.3 Two-Dimensional Shape Function 127\u003c\/p\u003e \u003cp\u003e8.4 Three-Dimensional Shape Function 130\u003c\/p\u003e \u003cp\u003e8.5 Coordinate Transformation 136\u003c\/p\u003e \u003cp\u003e8.6 Displacement Function 145\u003c\/p\u003e \u003cp\u003e8.7 Element Strain 147\u003c\/p\u003e \u003cp\u003e8.8 Stiffness Matrix 151\u003c\/p\u003e \u003cp\u003e8.9 Nodal Loads 153\u003c\/p\u003e \u003cp\u003e8.10 Degradation of Isoparametric Elements 155\u003c\/p\u003e \u003cp\u003e8.11 Numerical Integration 161\u003c\/p\u003e \u003cp\u003e8.13 Stress Refinement and Stress Smoothing 168\u003c\/p\u003e \u003cp\u003e8.14 Elemental Form and Layout 173\u003c\/p\u003e \u003cp\u003e8.15 Inconsistent Elements 176\u003c\/p\u003e \u003cp\u003e8.16 Patch Test 179\u003c\/p\u003e \u003cp\u003e8.17 Triangular, Tetrahedral, and Prismatic Curved-Side Elements 183\u003c\/p\u003e \u003cp\u003e8.18 Vector Computation in Isoparametric Elements 187\u003c\/p\u003e \u003cp\u003e8.19 Numerical Examples of Isoparametric Elements 191\u003c\/p\u003e \u003cp\u003e8.20 Infinite Elements 192\u003c\/p\u003e \u003cp\u003eBibliography 199\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Comparison and Application Instances of Various Planar and Spatial Elements 201\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Comparison and Selection of Various Planar Elements 201\u003c\/p\u003e \u003cp\u003e9.2 Comparison and Selection of Various Spatial Elements 205\u003c\/p\u003e \u003cp\u003e9.3 Analysis of Stresses in Arch Dam 209\u003c\/p\u003e \u003cp\u003e9.4 Analysis of Stress in Buttress Dam 215\u003c\/p\u003e \u003cp\u003e9.5 Analysis of Spatial Effect of Gravity Dam 217\u003c\/p\u003e \u003cp\u003e9.6 Analysis of Spatial Effect of Earth Dam 217\u003c\/p\u003e \u003cp\u003e9.7 Analysis of Stress on Tunnel Lining 220\u003c\/p\u003e \u003cp\u003eBibliography 221\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Elastic Thin Plate 223\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Bending of Elastic Thin Plate 223\u003c\/p\u003e \u003cp\u003e10.2 Rectangular Thin Plate Element 228\u003c\/p\u003e \u003cp\u003e10.3 TriangularThin Plate Element 235\u003c\/p\u003e \u003cp\u003e10.4 Plate Element with Curved Boundary and Deflection and Rotation Defined Respectively 241\u003c\/p\u003e \u003cp\u003e10.5 The Plate on Elastic Foundation 248\u003c\/p\u003e \u003cp\u003e10.5.1 Plate onWinkler Foundation 248\u003c\/p\u003e \u003cp\u003e10.5.2 Plate on Elastic Half Space 249\u003c\/p\u003e \u003cp\u003eBibliography 252\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Elastic Thin Shell 255\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Element Stiffness Matrix in Local Coordinate System 255\u003c\/p\u003e \u003cp\u003e11.2 Coordinate Transformation: Global Stiffness Matrix 259\u003c\/p\u003e \u003cp\u003e11.3 Direction Cosine of Local Coordinate 261\u003c\/p\u003e \u003cp\u003e11.4 Curved-Surface Shell Element 264\u003c\/p\u003e \u003cp\u003e11.5 Shell Supported or Reinforced by Curved Beam 268\u003c\/p\u003e \u003cp\u003e11.6 Example 271\u003c\/p\u003e \u003cp\u003eBibliography 271\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Axisymmetric Shell 273\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Linear Element 273\u003c\/p\u003e \u003cp\u003e12.2 Curved Element 277\u003c\/p\u003e \u003cp\u003eBibliography 280\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Problems in Fluid Mechanics 281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Relation between Stress and Strain for Newtonian Fluids 281\u003c\/p\u003e \u003cp\u003e13.2 Equation of Motion 283\u003c\/p\u003e \u003cp\u003e13.3 Continuity Equation 284\u003c\/p\u003e \u003cp\u003e13.4 Energy Equation 284\u003c\/p\u003e \u003cp\u003e13.5 State and Viscosity Equations 284\u003c\/p\u003e \u003cp\u003e13.6 Fundamental Equations for Steady Seepage Flow andTheir Discretization 285\u003c\/p\u003e \u003cp\u003e13.7 Free Surface Calculation for Seepage Analysis 290\u003c\/p\u003e \u003cp\u003e13.8 Substitution of the Curtain of Drainage Holes by the Seeping Layer for Seepage Analysis 296\u003c\/p\u003e \u003cp\u003e13.9 Unsteady Seepage Flow 300\u003c\/p\u003e \u003cp\u003e13.10 DynamicWater Pressure during Earthquake 301\u003c\/p\u003e \u003cp\u003e13.12 Potential Flow Formulated by Stream Function 𝜓 307\u003c\/p\u003e \u003cp\u003e13.13 Flow on the Free Surface 312\u003c\/p\u003e \u003cp\u003e13.14 Viscous and Non-Newtonian Flow 316\u003c\/p\u003e \u003cp\u003eBibliography 318\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Problems in Conduction of Heat in Solids 321\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Differential Equation: Initial and Boundary Conditions for Conductionof Heat in Solids 321\u003c\/p\u003e \u003cp\u003e14.2 Variational Principle for Conduction of Heat in Solids 322\u003c\/p\u003e \u003cp\u003e14.3 Discretization of Continuous Body 323\u003c\/p\u003e \u003cp\u003e14.4 Fundamental Equations for Solving Unsteady Temperature Field by FEM 324\u003c\/p\u003e \u003cp\u003e14.5 Two-Dimensional Unsteady Temperature Field, Triangular Elements 327\u003c\/p\u003e \u003cp\u003e14.6 Isoparametric Elements 329\u003c\/p\u003e \u003cp\u003e14.7 Computing Examples of Unsteady Temperature Field 331\u003c\/p\u003e \u003cp\u003e14.8 Temperature Field of Mass Concrete with Pipe Cooling 332\u003c\/p\u003e \u003cp\u003eBibliography 335\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Methods for Nonlinear Finite Element Analysis 337\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 IncrementalMethod 338\u003c\/p\u003e \u003cp\u003e15.2 Iterative Method 342\u003c\/p\u003e \u003cp\u003e15.3 Mixed Method 349\u003c\/p\u003e \u003cp\u003e15.4 Application of Substructure Method in Nonlinear Analysis 349\u003c\/p\u003e \u003cp\u003eBibliography 351\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Problems in Theory of Plasticity 353\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 One-Dimensional Stress–Strain Relation 353\u003c\/p\u003e \u003cp\u003e16.2 Decompose of Stress Tensor and Stress Invariant 355\u003c\/p\u003e \u003cp\u003e16.3 Haigh–Westergaard Stress Space 357\u003c\/p\u003e \u003cp\u003e16.4 Decompose of Strain Tensor 362\u003c\/p\u003e \u003cp\u003e16.5 Criterion of Yield 363\u003c\/p\u003e \u003cp\u003e16.6 Strain Hardening 379\u003c\/p\u003e \u003cp\u003e16.7 Criterion of Loading and Unloading 382\u003c\/p\u003e \u003cp\u003e16.8 The Finite Element Method in Elastic–Plastic Incremental Theory 384\u003c\/p\u003e \u003cp\u003e16.9 Finite Element Method in the Full VariableTheory of Plasticity 397\u003c\/p\u003e \u003cp\u003e16.10 Practical Simplified Models for Nonlinear Problem of Material 399\u003c\/p\u003e \u003cp\u003eBibliography 404\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Creep of Concrete and its Influence on Stresses and Deformations of Structures 407\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Stress–Strain Relation of Concrete 407\u003c\/p\u003e \u003cp\u003e17.2 Influence of Creep on Stresses and Deformations of Linear Elastocreeping Body 416\u003c\/p\u003e \u003cp\u003e17.3 Analysis of Elastocreeping Stresses of Concrete Structure 419\u003c\/p\u003e \u003cp\u003e17.4 Compound Layer Element for the Simulation Analysis of Concrete Dams 424\u003c\/p\u003e \u003cp\u003eBibliography 429\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Stress Analysis for Viscoelastic and Visco-Plastic Bodies 431\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 The Stress–Strain Relation of Viscoelastic Body under the Action of Unidirectional Stress 431\u003c\/p\u003e \u003cp\u003e18.2 The Stress–Strain Relation under the Action of Complex Stresses 434\u003c\/p\u003e \u003cp\u003e18.3 Stress Analysis of Viscoelastic Body 436\u003c\/p\u003e \u003cp\u003e18.4 Effective Modulus Method and Equivalent Temperature Method for Simple Harmonic Temperature Creep Stress Analysis of Concrete at Late Ages and Viscoelastic Body 439\u003c\/p\u003e \u003cp\u003e18.5 Stress Analysis for Visco-Plastic Bodies 441\u003c\/p\u003e \u003cp\u003e18.6 Combined Viscoelastic–Plastic Models 449\u003c\/p\u003e \u003cp\u003eBibliography 451\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Elastic Stability Problem 453\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Geometrical Stiffness Matrix of the Beam Element 453\u003c\/p\u003e \u003cp\u003e19.2 Geometrical Stiffness Matrix of Plate Elements 457\u003c\/p\u003e \u003cp\u003e19.3 Global Analysis 459\u003c\/p\u003e \u003cp\u003e19.4 Cases of Beam System 461\u003c\/p\u003e \u003cp\u003e19.5 Computing Examples of Elastic Stability of Thin Plate System 462\u003c\/p\u003e \u003cp\u003eBibliography 465\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Problems in Analysis of Structures with Large Displacement 467\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 The Basic Method for Geometrical Nonlinear Problems 467\u003c\/p\u003e \u003cp\u003e20.2 The Plate Element of Large Deflection 471\u003c\/p\u003e \u003cp\u003e20.3 Three-Dimensional Solid Element of Large Displacement 476\u003c\/p\u003e \u003cp\u003e20.4 Double Nonlinearity: Elastoplastic Large Displacement Problem 478\u003c\/p\u003e \u003cp\u003eBibliography 478\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Problems in Fracture Mechanics 481\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Introduction 481\u003c\/p\u003e \u003cp\u003e21.2 Direct Method 484\u003c\/p\u003e \u003cp\u003e21.3 J-Integral Method 486\u003c\/p\u003e \u003cp\u003e21.4 Energy Method, FlexibilityMethod, and Bueckner Formula 490\u003c\/p\u003e \u003cp\u003e21.5 Stiffness DerivativeMethod 494\u003c\/p\u003e \u003cp\u003e21.6 Singular Element of the Crack Tip 499\u003c\/p\u003e \u003cp\u003e21.7 Singular Isoparametric Element (1\/4 Length Midpoint Method) 502\u003c\/p\u003e \u003cp\u003e21.8 Blunt Crack Zone Model 506\u003c\/p\u003e \u003cp\u003e21.9 Elastic–Plastic Fracture 509\u003c\/p\u003e \u003cp\u003e21.10 Extended Finite Element Method for Fracture Analysis 512\u003c\/p\u003e \u003cp\u003eBibliography 514\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Problems in Structural Dynamics 515\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Equations of Motion 515\u003c\/p\u003e \u003cp\u003e22.2 Mass Matrix 516\u003c\/p\u003e \u003cp\u003e22.3 Damping Matrix 522\u003c\/p\u003e \u003cp\u003e22.4 Natural Frequency and Vibration Mode of Structure 526\u003c\/p\u003e \u003cp\u003e22.5 Mode Superposition Method for Analyzing the Structure of Forced Vibration 535\u003c\/p\u003e \u003cp\u003e22.6 Dynamic Response of Structure under the Action of Earthquake Solving by Vibration Mode Superposition Method 536\u003c\/p\u003e \u003cp\u003e22.7 Vector IterationMethod for Computing the Natural Frequency and Vibration Mode 538\u003c\/p\u003e \u003cp\u003e22.8 Energy Method for Computing the Natural Frequencies of Structure 545\u003c\/p\u003e \u003cp\u003e22.9 Subspace Iteration Method for Computing the Natural Frequencies and Vibration Modes of Structure 548\u003c\/p\u003e \u003cp\u003e22.10 Ritz Vector Superposition Method for Solving Forced Vibration of Structure 554\u003c\/p\u003e \u003cp\u003e22.11 Modified Ritz Vector Superposition Method 556\u003c\/p\u003e \u003cp\u003e22.12 Dynamic Substructure Method 557\u003c\/p\u003e \u003cp\u003e22.13 Direct Integration Method for Solving the Equation of Motion 560\u003c\/p\u003e \u003cp\u003e22.14 Coupled Vibration of Solid and Fluid 570\u003c\/p\u003e \u003cp\u003e22.15 Seismic Stress of Gravity Dam 571\u003c\/p\u003e \u003cp\u003e22.16 Seismic Stress of Buttress Dam 574\u003c\/p\u003e \u003cp\u003e22.17 Vibration of Arch Dam 575\u003c\/p\u003e \u003cp\u003e22.18 Seismic Stress of Earth Dam 575\u003c\/p\u003e \u003cp\u003e22.19 Seismic Stresses of Cylindrical Shell 577\u003c\/p\u003e \u003cp\u003e22.20 Nonlinear Dynamic Responses of Underground Structures 578\u003c\/p\u003e \u003cp\u003eBibliography 580\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Problems in Rock Mechanics 581\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Structure of Rock 581\u003c\/p\u003e \u003cp\u003e23.2 Equivalent Deformation Modulus 583\u003c\/p\u003e \u003cp\u003e23.3 Two-Dimensional Linear Joint Element 584\u003c\/p\u003e \u003cp\u003e23.4 Stiffness Coefficients of Joint Element 587\u003c\/p\u003e \u003cp\u003e23.5 Layer Element 591\u003c\/p\u003e \u003cp\u003e23.6 Two-Dimensional High-Order Joint Element 593\u003c\/p\u003e \u003cp\u003e23.7 Three-Dimensional Joint Element 597\u003c\/p\u003e \u003cp\u003e23.8 Infinite Joint Element 602\u003c\/p\u003e \u003cp\u003e23.9 Choice of Method for Stress Analysis in Rock 605\u003c\/p\u003e \u003cp\u003e23.10 Elastic Increment Method for Nonlinear Stress Analysis 606\u003c\/p\u003e \u003cp\u003e23.11 Initial Stress Method and No Tension Method 608\u003c\/p\u003e \u003cp\u003e23.12 Elastic–Plastic Increment Method 612\u003c\/p\u003e \u003cp\u003e23.13 Viscoelastic–Plastic Method 616\u003c\/p\u003e \u003cp\u003e23.14 Computation of Anchor Bolt in Rock Foundation 618\u003c\/p\u003e \u003cp\u003e23.15 Computing Examples in Rock Mechanics 621\u003c\/p\u003e \u003cp\u003eBibliography 626\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 Problems in Soil Mechanics 627\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 Nonlinear Elastic Model 627\u003c\/p\u003e \u003cp\u003e24.2 Elastic–Plastic Model with Two Yield Surfaces 633\u003c\/p\u003e \u003cp\u003e24.3 Interaction between Soil and Structure: Contact Element 637\u003c\/p\u003e \u003cp\u003e24.4 Consolidation of Soil 640\u003c\/p\u003e \u003cp\u003e24.5 Stress, Deformation, and Stability of Earth Dam 648\u003c\/p\u003e \u003cp\u003e24.6 Computation of Rockfill Dam with Concrete Face Slab 649\u003c\/p\u003e \u003cp\u003e24.7 Limit Analysis in Rock and Soil Mechanics 652\u003c\/p\u003e \u003cp\u003eBibliography 657\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 Plain and Reinforced Concrete Structures 659\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e25.1 Constitutive Models of Concrete 660\u003c\/p\u003e \u003cp\u003e25.2 Finite Element Models for Cracks in Concrete 672\u003c\/p\u003e \u003cp\u003e25.3 The Calculation of the Smeared Crack Model 682\u003c\/p\u003e \u003cp\u003e25.4 The Constitutive Relation and the Stress Calculation of the Steel 691\u003c\/p\u003e \u003cp\u003e25.5 The Finite Element Model of the Steel Bar 692\u003c\/p\u003e \u003cp\u003e25.6 The Connection of the Steel Bar and Concrete 693\u003c\/p\u003e \u003cp\u003e25.7 The Bond Stress between the Steel Bar and Concrete:The Stiffness Coefficient of the Linking Spring and the Contact Element 696\u003c\/p\u003e \u003cp\u003e25.8 The Stiffness Matrix of the Reinforced Concrete Structure 698\u003c\/p\u003e \u003cp\u003e25.9 The Calculation of Steel Bar in the Isoparametric Element 698\u003c\/p\u003e \u003cp\u003e25.10 The Layered Element of the Reinforced Concrete Plates and Shells 706\u003c\/p\u003e \u003cp\u003eBibliography 709\u003c\/p\u003e \u003cp\u003e26 Back Analysis of Engineering 711\u003c\/p\u003e \u003cp\u003e26.1 General Principles of Back Analysis 711\u003c\/p\u003e \u003cp\u003e26.2 Back Analysis of the Seepage Field 712\u003c\/p\u003e \u003cp\u003e26.3 Elastic Displacement Back Analysis of Homogeneous Body and Proportional Deformation Heterogeneous Body 716\u003c\/p\u003e \u003cp\u003e26.4 Back Analysis of Material Parameters of Heterogeneous Elastic Body 722\u003c\/p\u003e \u003cp\u003e26.5 Back Analysis of Interaction of Elastic Structure with the Surrounding Medium 728\u003c\/p\u003e \u003cp\u003e26.6 Nonlinear Solid Back Analysis 733\u003c\/p\u003e \u003cp\u003eBibliography 737\u003c\/p\u003e \u003cp\u003e\u003cb\u003e27 Automatic Mesh Generation, Error Estimation, and Auto-adaptation Technique 739\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e27.1 Automatic Generation of Computing Grid 740\u003c\/p\u003e \u003cp\u003e27.2 Error Estimation 742\u003c\/p\u003e \u003cp\u003e27.3 Auto-adaptation Technique: h Method 745\u003c\/p\u003e \u003cp\u003e27.4 Auto-adaptation Technique: p Method 746\u003c\/p\u003e \u003cp\u003eBibliography 748\u003c\/p\u003e \u003cp\u003e\u003cb\u003e28 Matrix 751\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e28.1 Definition of Matrix 751\u003c\/p\u003e \u003cp\u003e28.2 Principal Types of Matrix 752\u003c\/p\u003e \u003cp\u003e28.3 Equality, Addition, and Subtraction of Matrices 755\u003c\/p\u003e \u003cp\u003e28.4 Matrix Multiplied by a Number 756\u003c\/p\u003e \u003cp\u003e28.5 Multiplication of Matrices 757\u003c\/p\u003e \u003cp\u003e28.6 Determinant 760\u003c\/p\u003e \u003cp\u003e28.7 Inverse Matrix 763\u003c\/p\u003e \u003cp\u003e28.8 Partitioned Matrix 766\u003c\/p\u003e \u003cp\u003e28.9 Orthogonal Matrix 770\u003c\/p\u003e \u003cp\u003e28.10 Positive Definite Matrix 771\u003c\/p\u003e \u003cp\u003e28.11 Derivative of Matrix 772\u003c\/p\u003e \u003cp\u003e28.12 Integration of Matrix 774\u003c\/p\u003e \u003cp\u003eBibliography 775\u003c\/p\u003e \u003cp\u003e\u003cb\u003e29 Linear Algebraic Equation Set 777\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e29.1 Linear Algebraic Equation Set 777\u003c\/p\u003e \u003cp\u003e29.2 Simple IterativeMethod 778\u003c\/p\u003e \u003cp\u003e29.3 Seidel Iterative Method 780\u003c\/p\u003e \u003cp\u003e29.4 Over-Relaxation IterativeMethod 781\u003c\/p\u003e \u003cp\u003e29.5 Block Over-Relaxation Iterative Method 781\u003c\/p\u003e \u003cp\u003e29.6 Direct Solution Method 783\u003c\/p\u003e \u003cp\u003e29.7 Conjugate Gradient Method 788\u003c\/p\u003e \u003cp\u003e29.8 Comparison of Several Kinds of Commonly Used Method 790\u003c\/p\u003e \u003cp\u003e29.9 Homogeneous Linear Equations 791\u003c\/p\u003e \u003cp\u003eBibliography 792\u003c\/p\u003e \u003cp\u003e\u003cb\u003e30 Variational Method 793\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e30.1 The Extrema of Functions 793\u003c\/p\u003e \u003cp\u003e30.2 The Extrema of Functionals 795\u003c\/p\u003e \u003cp\u003e30.3 Preliminary Theorems 796\u003c\/p\u003e \u003cp\u003e30.4 Euler’s Equation of One-Dimensional Problems 797\u003c\/p\u003e \u003cp\u003e30.5 Euler’s Equation for Plane Problems 800\u003c\/p\u003e \u003cp\u003e30.6 Euler’s Equations of Spatial Problems 803\u003c\/p\u003e \u003cp\u003e30.7 Ritz Method for Solving Variational Problems 806\u003c\/p\u003e \u003cp\u003e30.8 Finite Element Method for Solving the Variational Problems 809\u003c\/p\u003e \u003cp\u003eBibliography 811\u003c\/p\u003e \u003cp\u003e31 Weighted Residual Method 813\u003c\/p\u003e \u003cp\u003e31.1 Introduction toWeighted Residual Method 813\u003c\/p\u003e \u003cp\u003e31.2 Weight Function for Internal Residual Method 814\u003c\/p\u003e \u003cp\u003e31.3 Establish Fundamental Equations of Finite Element Method byWeighted Residual Method 820\u003c\/p\u003e \u003cp\u003e31.4 Twist of Elastic Column 824\u003c\/p\u003e \u003cp\u003e31.5 Unsteady Temperature Field 828\u003c\/p\u003e \u003cp\u003e31.6 Dynamic Response of Structure 832\u003c\/p\u003e \u003cp\u003eBibliography 834\u003c\/p\u003e \u003cp\u003eAppendix A 835\u003c\/p\u003e \u003cp\u003eAppendix B 839\u003c\/p\u003e \u003cp\u003eIndex 841\u003c\/p\u003e   \u003cp\u003e \u003cstrong\u003eAbout the Author\u003c\/strong\u003e\u003cbr\u003e \u003cstrong\u003eBofang Zhu,\u003c\/strong\u003e China Institute of Water Resources and Hydropower Research, Chinese Academy of Engineering, China      \u003c\/p\u003e\u003cp\u003e A comprehensive review of the Finite Element Method (FEM), this book provides the fundamentals together with a wide range of applications in civil, mechanical and aeronautical engineering. It addresses both the theoretical and numerical implementation aspects of the FEM, providing examples in several important topics such as solid mechanics, fluid mechanics and heat transfer, appealing to a wide range of engineering disciplines.    \u003c\/p\u003e\u003cul\u003e \u003cli\u003eOffers a systematic look at Finite Element Method from a classical perspective\u003c\/li\u003e \u003cli\u003eFeatures multidisciplinary applications that demonstrate the method in an accessible manner\u003c\/li\u003e \u003cli\u003ePresents an extensive range of topics from solid mechanics, fluid mechanics, heat transfer, dynamics and stability, and civil engineering\u003c\/li\u003e \u003cli\u003eAccompanying website to include problems and exercises \u003cstrong\u003ewww.wiley.com\/go\/zhufem17\u003c\/strong\u003e\n\u003c\/li\u003e \u003c\/ul\u003e \u003cbr\u003e  \u003cp\u003e Written by a renowned author and academician with the Chinese Academy of Engineering, \u003cem\u003eThe Finite Element Method\u003c\/em\u003e would appeal to researchers looking to understand how the fundamentals of the FEM can be applied in other disciplines. Researchers and graduate students studying hydraulic, mechanical and civil engineering will find it a practical reference text.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47990228844773,"sku":"NP9781119107316","price":177.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119107316.jpg?v=1761786990","url":"https:\/\/k12savings.com\/products\/the-finite-element-method-isbn-9781119107316","provider":"K12savings","version":"1.0","type":"link"}